Right isosceles triangle

Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?

Correct result:

S =  25 cm²

Solution:

$$\begin{gathered} c_1=5\text{ cm } \\ {c}_2=c_1=5=5\text{ cm } \\ c=c_1+c_2=5+5=10\text{ cm } \\ h=\sqrt{c_1\cdot c_2}=\sqrt{5\cdot 5}=5\text{ cm } \\ S={\displaystyle \frac{c\cdot h}{2}}={\displaystyle \frac{10\cdot 5}{2}}=25{\text{cm}}^2 \end{gathered}$$

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